BIP 0038

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  BIP: 38
  Title: Passphrase-protected private key
  Author: Mike Caldwell
  Status: Draft
  Type: Standards Track
  Created: 20-11-2012

Abstract

A method is proposed for encrypting and encoding a passphrase-protected Bitcoin private key record in the form of a 58-character Base58Check-encoded printable string. Encrypted private key records are intended for use on paper wallets and physical Bitcoins. Each record string contains all the information needed to reconstitute the private key except for a passphrase, and the methodology uses salting and scrypt to resist brute-force attacks.

The method provides two encoding methodologies - one permitting any known private key to be encrypted with any passphrase, and another permitting a shared private key generation scheme where the party generating the final key string and its associated Bitcoin address (such as a physical bitcoin manufacturer) knows only a string derived from the original passphrase, and where the original passphrase is needed in order to actually redeem funds sent to the associated Bitcoin address.

A 32-bit hash of the resulting Bitcoin address is encoded in plaintext within each encrypted key, so it can be correlated to a Bitcoin address with reasonable probability by someone not knowing the passphrase. The complete Bitcoin address can be derived through successful decryption of the key record.

Motivation

The motivation to make this proposal stems from observations of the way physical bitcoins and paper wallets are used.

An issuer of physical bitcoins must be trustworthy and trusted. Even if trustworthy, users are rightful to be skeptical about a third party with theoretical access to take their funds. A physical bitcoin that cannot be compromised by its issuer is always more intrinsically valuable than one that can.

A two-factor physical bitcoin solution is highly useful to individuals and institutions wishing to securely own bitcoins without any risk of electronic theft and without the responsibility of climbing the technological learning curve necessary to produce such an environment themselves. Two-factor physical bitcoins allow a secure storage solution to be put in a box and sold on the open market, greatly enlarging the number of people who are able to securely store bitcoins.

Existing methodologies for creating two-factor physical bitcoins are limited and cumbersome. At the time of this proposal, a user could create their own private key, submit the public key to the physical bitcoin issuer, and then receive a physical bitcoin that must be kept together with some sort of record of the user-generated private key, and finally, must be redeemed through a tool. The fact that the physical bitcoin must be kept together with a user-produced private key negates much of the benefit of the physical bitcoin - the user may as well just print and maintain a private key.

A standardized password-protected private key format makes acquiring and redeeming two-factor physical bitcoins simpler for the user. Instead of maintaining a private key that cannot be memorized, the user may choose a passphrase of their choice. The passphrase may be much shorter than the length of a typical private key, short enough that they could use a label or engraver to permanently commit their passphrase to their physical Bitcoin piece once they have received it. By adopting a standard way to encrypt a private key, we maximize the possibility that they'll be able to redeem their funds in the venue of their choice, rather than relying on an executable redemption tool they may not wish to download.

Password and passphrase-protected private keys enable new practical use cases for sending bitcoins from person to person. Someone wanting to send bitcoins through postal mail could send a password-protected paper wallet and give the recipient the passphrase over the phone or e-mail, making the transfer safe from interception of either channel. A user of paper wallets or Bitcoin banknote-style vouchers ("cash") could carry funded encrypted private keys while leaving a copy at home as an element of protection against accidental loss or theft. A user of paper wallets who leaves bitcoins in a bank vault or safety deposit box could keep the password at home or share it with trusted associates as protection against someone at the bank gaining access to the paper wallets and spending from them. The foreseeable and unforeseeable use cases for password-protected private keys are numerous.

Copyright

This proposal is hereby placed in the public domain.

Rationale

User story: As a Bitcoin user who uses paper wallets, I would like the ability to add encryption, so that my Bitcoin paper storage can be two factor: something I have plus something I know.
User story: As a Bitcoin user who would like to pay a person or a company with a private key, I do not want to worry that any part of the communication path may result in the interception of the key and theft of my funds. I would prefer to offer an encrypted private key, and then follow it up with the password using a different communication channel (e.g. a phone call or SMS).
User story: (EC-multiplied keys) As a user of physical bitcoins, I would like a third party to be able to create password-protected Bitcoin private keys for me, without them knowing the password, so I can benefit from the physical bitcoin without the issuer having access to the private key. I would like to be able to choose a password whose minimum length and required format does not preclude me from memorizing it or engraving it on my physical bitcoin, without exposing me to an undue risk of password cracking and/or theft by the manufacturer of the item.
User story: (EC multiplied keys) As a user of paper wallets, I would like the ability to generate a large number of Bitcoin addresses protected by the same password, while enjoying a high degree of security (highly expensive scrypt parameters), but without having to incur the scrypt delay for each address I generate.

Specification

This proposal makes use of the following functions and definitions:

  • AES256Encrypt, AES256Decrypt: the simple form of the well-known AES block cipher without consideration for initialization vectors or block chaining. Each of these functions takes a 256-bit key and 16 bytes of input, and deterministically yields 16 bytes of output.
  • SHA256, a well-known hashing algorithm that takes an arbitrary number of bytes as input and deterministically yields a 32-byte hash.
  • scrypt: A well-known key derivation algorithm. It takes the following parameters: (string) password, (string) salt, (int) n, (int) r, (int) p, (int) length, and deterministically yields an array of bytes whose length is equal to the length parameter.
  • ECMultiply: Multiplication of an elliptic curve point by a scalar integer with respect to the secp256k1 elliptic curve.
  • G, N: Constants defined as part of the secp256k1 elliptic curve. G is an elliptic curve point, and N is a large positive integer.
  • Base58Check: a method for encoding arrays of bytes using 58 alphanumeric characters commonly used in the Bitcoin ecosystem.

Prefix

It is proposed that the resulting Base58Check-encoded string start with a '6'. The number '6' is intended to represent, from the perspective of the user, "a private key that needs something else to be usable" - an umbrella definition that could be understood in the future to include keys participating in multisig transactions, and was chosen with deference to the existing prefix '5' most commonly observed in Wallet Import Format which denotes an unencrypted private key.

It is proposed that the second character ought to give a hint as to what is needed as a second factor, and for an encrypted key requiring a passphrase, the uppercase letter P is proposed.

To keep the size of the encrypted key down, no initialization vectors (IVs) are used in the AES encryption. Rather, suitable values for IV-like use are derived using scrypt from the passphrase and from using a 32-bit hash of the resulting Bitcoin address as salt.

Proposed specification

  • Object identifier prefix: 0x0142 (non-EC-multiplied) or 0x0143 (EC-multiplied). These are constant bytes that appear at the beginning of the Base58Check-encoded record, and their presence causes the resulting string to have a predictable prefix.
  • How the user sees it: 58 characters always starting with '6P'
    • Visual cues are present in the third character for visually identifying the EC-multiply and compress flag.
  • Count of payload bytes (beyond prefix): 37
    • 1 byte (flagbyte):
      • the most significant two bits are set as follows to preserve the visibility of the compression flag in the prefix, as well as to keep the payload within the range of allowable values that keep the "6P" prefix intact. For non-EC-multiplied keys, the bits are 11. For EC-multiplied keys, the bits are 00.
      • the bit with value 0x20 when set indicates the key should be converted to a bitcoin address using the compressed public key format.
      • the bits with values 0x10 and 0x08 are reserved for a future specification that contemplates using multisig as a way to combine the factors such that parties in possession of the separate factors can independently sign a proposed transaction without requiring that any party possess both factors. These bits must be 0 to comply with this version of the specification.
      • the bit with value 0x04 selects one of two methods for introducing ownerentropy into the key derivation process. This applies to EC-multiplied keys only. Must be 0 for non-EC-multiplied keys.
      • remaining bits are reserved for future use and must all be 0 to comply with this version of the specification.
    • 4 bytes: SHA256(SHA256(expected_bitcoin_address))[0...3], used both for typo checking and as salt
    • 16 bytes: Contents depend on whether EC multiplication is used.
    • 16 bytes: lasthalf: An AES-encrypted key material record (contents depend on whether EC multiplication is used)
  • Range in base58check encoding for non-EC-multiplied keys without compression (prefix 6PR):
    • Minimum value: 6PRHv1jg1ytiE4kT2QtrUz8gEjMQghZDWg1FuxjdYDzjUkcJeGdFj9q9Vi (based on 01 42 C0 plus thirty-six 00's)
    • Maximum value: 6PRWdmoT1ZursVcr5NiD14p5bHrKVGPG7yeEoEeRb8FVaqYSHnZTLEbYsU (based on 01 42 C0 plus thirty-six FF's)
  • Range in base58check encoding for non-EC-multiplied keys with compression (prefix 6PY):
    • Minimum value: 6PYJxKpVnkXUsnZAfD2B5ZsZafJYNp4ezQQeCjs39494qUUXLnXijLx6LG (based on 01 42 E0 plus thirty-six 00's)
    • Maximum value: 6PYXg5tGnLYdXDRZiAqXbeYxwDoTBNthbi3d61mqBxPpwZQezJTvQHsCnk (based on 01 42 E0 plus thirty-six FF's)
  • Range in base58check encoding for EC-multiplied keys without compression (prefix 6Pf):
    • Minimum value: 6PfKzduKZXAFXWMtJ19Vg9cSvbFg4va6U8p2VWzSjtHQCCLk3JSBpUvfpf (based on 01 43 00 plus thirty-six 00's)
    • Maximum value: 6PfYiPy6Z7BQAwEHLxxrCEHrH9kasVQ95ST1NnuEnnYAJHGsgpNPQ9dTHc (based on 01 43 00 plus thirty-six FF's)
  • Range in base58check encoding for non-EC-multiplied keys with compression (prefix 6Pn):
    • Minimum value: 6PnM2wz9LHo2BEAbvoGpGjMLGXCom35XwsDQnJ7rLiRjYvCxjpLenmoBsR (based on 01 43 20 plus thirty-six 00's)
    • Maximum value: 6PnZki3vKspApf2zym6Anp2jd5hiZbuaZArPfa2ePcgVf196PLGrQNyVUh (based on 01 43 20 plus thirty-six FF's)

Encryption when EC multiply flag is not used

Encrypting a private key without the EC multiplication offers the advantage that any known private key can be encrypted. The party performing the encryption must know the passphrase.

Encryption steps:

  1. Compute the Bitcoin address (ASCII), and take the first four bytes of SHA256(SHA256()) of it. Let's call this "addresshash".
  2. Derive a key from the passphrase using scrypt
    • Parameters: passphrase is the passphrase itself encoded in UTF-8. addresshash came from the earlier step, n=16384, r=8, p=8, length=64 (n, r, p are provisional and subject to consensus)
    • Let's split the resulting 64 bytes in half, and call them derivedhalf1 and derivedhalf2.
  3. Do AES256Encrypt(bitcoinprivkey[0...15] xor derivedhalf1[0...15], derivedhalf2), call the 16-byte result encryptedhalf1
  4. Do AES256Encrypt(bitcoinprivkey[16...31] xor derivedhalf1[16...31], derivedhalf2), call the 16-byte result encryptedhalf2

The encrypted private key is the Base58Check-encoded concatenation of the following, which totals 39 bytes without Base58 checksum:

  • 0x01 0x42 + flagbyte + salt + encryptedhalf1 + encryptedhalf2

Decryption steps:

  1. Collect encrypted private key and passphrase from user.
  2. Derive derivedhalf1 and derivedhalf2 by passing the passphrase and addresshash into scrypt function.
  3. Decrypt encryptedhalf1 and encryptedhalf2 using AES256Decrypt, merge them to form the encrypted private key.
  4. Convert that private key into a Bitcoin address, honoring the compression preference specified in flagbyte of the encrypted key record.
  5. Hash the Bitcoin address, and verify that addresshash from the encrypted private key record matches the hash. If not, report that the passphrase entry was incorrect.

Encryption when EC multiply mode is used

Encrypting a private key with EC multiplication offers the ability for someone to generate encrypted keys knowing only an EC point derived from the original passphrase and some salt generated by the passphrase's owner, and without knowing the passphrase itself. Only the person who knows the original passphrase can decrypt the private key. This methodology does not offer the ability to encrypt a known private key - this means that the process of creating encrypted keys is also the process of generating new addresses.

Using EC multiply also allows a passphrase to be protected once by very expensive scrypt parameters, and then the protected passphrase be used to trivially generate large numbers of Bitcoin keypairs protected with the same passphrase without a correspondingly-expensive per-keypair delay or resource cost.

Steps performed by the person with the passphrase (call him the owner):

  1. Generate 8 bytes of random numbers, call them ownerentropy. Divide it into two halves, called ownersaltA and ownersaltB.
  2. Derive a key from the passphrase using scrypt
    • Parameters: passphrase is the passphrase itself encoded in UTF-8. salt is ownersaltA. n=16384, r=8, p=8, length=32.
    • Call the resulting 32 bytes prefactor.
    • Take SHA256(SHA256(prefactor + ownersaltB)) and call this passfactor.
  3. Compute the elliptic curve point G * passfactor, and convert the result to compressed notation (33 bytes). Call this passpoint. Compressed notation is used for this purpose regardless of whether the intent is to create Bitcoin addresses with or without compressed public keys.
  4. Convey ownersalt and passpoint to the party generating the keys, along with a checksum to ensure integrity.
    • The following Base58Check-encoded format is recommended for this purpose: bytes "2C E9 B3 E1 FF 39 E2 51" followed by ownersaltA, ownersaltB, and then passpoint. The resulting string will start with the word "passphrase" due to the constant bytes, will be 72 characters in length, and encodes 49 bytes (8 bytes constant + 8 bytes ownersalt + 33 bytes passpoint). The checksum is handled in the Base58Check encoding. The resulting string is called intermediate_passphrase_string.

NOTE: The methodology for creating an intermediate code was recently modified to introduce ownersaltB. This permits rapid generation of batches of unique intermediate codes on mobile devices, allowing them to have a unique passfactor but without having to repeat the scrypt computation for each one. Summary of the differences: the magic ended in 0x53 instead of 0x51; the entirety of ownerentropy was given to scrypt as salt rather than just the first four bytes, and the double SHA256 step was skipped (so "passfactor" was the output of scrypt). Deprecation of the old methodology is recommended.

Steps to create new encrypted private keys given intermediate_passphrase_string from owner (so we have ownersaltA, ownersaltB, and passpoint, but we do not have passfactor or the passphrase):

  1. Set flagbyte to 0x04 (or 0x24 if generating Bitcoin address with compressed public key)
  2. Generate 24 random bytes, call this seedb. Take SHA256(SHA256(seedb)) to yield 32 bytes, call this factorb.
  3. ECMultiply passpoint by factorb. Use the resulting EC point as a public key and hash it into a Bitcoin address using either compressed or uncompressed public key methodology (specify which methodology is used inside flagbyte). This is the generated Bitcoin address, call it generatedaddress.
  4. Take the first four bytes of SHA256(SHA256(generatedaddress)) and call it addresshash.
  5. Now we will encrypt seedb. Derive a second key from passpoint using scrypt
    • Parameters: passphrase is passpoint provided from the first party (expressed in binary as 33 bytes). salt is addresshash + ownersaltA + ownersaltB, n=1024, r=1, p=1, length=64 (n, r, p are provisional and subject to consensus). The "+" operator is concatenation.
    • Split the result into two 16-byte halves and call them derivedhalf1 and derivedhalf2.
  6. Do AES256Encrypt(seedb[0...15]] xor derivedhalf1[0...15], derivedhalf2), call the 16-byte result encryptedpart1
  7. Do AES256Encrypt((encryptedpart1[8...15] + seedb[16...23]) xor derivedhalf1[16...31], derivedhalf2), call the 16-byte result encryptedseedb. The "+" operator is concatenation.

The encrypted private key is the Base58Check-encoded concatenation of the following, which totals 39 bytes without Base58 checksum:

  • 0x01 0x43 + flagbyte + addresshash + ownersaltA + ownersaltB + encryptedpart1[0...7] + encryptedpart2
Confirmation code

The party generating the Bitcoin address has the option to return a confirmation code back to owner which allows owner to independently verify that he has been given a Bitcoin address that actually depends on his passphrase. This protects owner from being given a Bitcoin address by the second party that is unrelated to the key derivation and possibly spendable by the second party. If a Bitcoin address given to owner can be successfully regenerated through the confirmation process, owner can be reasonably assured that any spending without the passphrase is infeasible. This confirmation code is 75 characters starting with "cfrm38".

To generate it, we need flagbyte, ownersaltA, ownersaltB, factorb, derivedhalf1 and derivedhalf2 from the original encryption operation.

  1. ECMultiply factorb by G, call the result pubfactorb. The result is 33 bytes.
  2. The first byte is 0x02 or 0x03. XOR it by (derivedhalf2[31] & 0x01), call the resulting byte pubfactorprefix.
  3. Do AES256Encrypt(pubfactor[1...16] xor derivedhalf1[0...15], derivedhalf2) and call the result pubfactorx1.
  4. Do AES256Encrypt(pubfactor[17...32] xor derivedhalf1[16...31], derivedhalf2) and call the result pubfactorx2.
  5. Concatenate pubfactorprefix + pubfactorx1 + pubfactorx2 (total 33 bytes) and call the result encryptedpubfactor.

The result is a Base58Check-encoded concatenation of the following:

  • 0x64 0x3B 0xF6 0xA8 0x9A + flagbyte + ownersaltA + ownersaltB + addresshash + encryptedpubfactor

A confirmation tool, given a passphrase and a confirmation code, can recalculate the address, verify the address hash, and then assert the following: "It is confirmed that Bitcoin address address depends on this passphrase".

Decryption
  1. Collect encrypted private key and passphrase from user.
  2. Derive passfactor using scrypt with ownersalt and the user's passphrase and use it to recompute passpoint
  3. Derive decryption key for seedb using scrypt with passpoint, addresshash, and ownersalt
  4. Decrypt encryptedpart2 using AES256Decrypt to yield the last 8 bytes of seedb and the last 8 bytes of encryptedpart1.
  5. Decrypt encryptedpart1 to yield the remainder of seedb.
  6. Use seedb to compute factorb.
  7. Multiply passfactor by factorb mod N to yield the private key associated with generatedaddress.
  8. Convert that private key into a Bitcoin address, honoring the compression preference specified in the encrypted key.
  9. Hash the Bitcoin address, and verify that addresshash from the encrypted private key record matches the hash. If not, report that the passphrase entry was incorrect.

Backwards compatibility

Backwards compatibility is minimally applicable since this is a new standard that at most extends Wallet Import Format. It is assumed that an entry point for private key data may also accept existing formats of private keys (such as hexadecimal and Wallet Import Format); this draft uses a key format that cannot be mistaken for any existing one and preserves auto-detection capabilities.

Suggestions for implementers of proposal with alt-chains

If this proposal is accepted into alt-chains, it is requested that the unused flag bytes not be used for denoting that the key belongs to an alt-chain.

Alt-chain implementers should exploit the address hash for this purpose. Since each operation in this proposal involves hashing a text representation of a coin address which (for Bitcoin) includes the leading '1', an alt-chain can easily be denoted simply by using the alt-chain's preferred format for representing an address. Alt-chain implementers may also change the prefix such that encrypted addresses do not start with "6P".

Discussion item: scrypt parameters

This proposal leaves the scrypt parameters up in the air. The following items are proposed for consideration:

The main goal of scrypt is to reduce the feasibility of brute force attacks. It must be assumed that an attacker will be able to use an efficient implementation of scrypt. The parameters should force a highly efficient implementation of scrypt to wait a decent amount of time to slow attacks.

On the other hand, an unavoidably likely place where scrypt will be implemented is using slow interpreted languages such as javascript. What might take milliseconds on an efficient scrypt implementation may take seconds in javascript.

It is believed, however, that someone using a javascript implementation is probably dealing with codes by hand, one at a time, rather than generating or processing large batches of codes. Thus, a wait time of several seconds is acceptable to a user.

A private key redemption process that forces a server to consume several seconds of CPU time would discourage implementation by the server owner, because they would be opening up a denial of service avenue by inviting users to make numerous attempts to invoke the redemption process. However, it's also feasible for the server owner to implement his redemption process in such a way that the decryption is done by the user's browser, offloading the task from his own server (and providing another reason why the chosen scrypt parameters should be tolerant of javascript-based decryptors).

The preliminary values of 16384, 8, and 8 are hoped to offer the following properties:

  • Encryption/decryption in javascript requiring several seconds per operation
  • Use of the parallelization parameter provides a modest opportunity for speedups in environments where concurrent threading is available - such environments would be selected for processes that must handle bulk quantities of encryption/decryption operations. Estimated time for an operation is in the tens or hundreds of milliseconds.

Reference implementation

Added to alpha version of Casascius Bitcoin Address Utility for Windows available at:

Click "Tools" then "PPEC Keygen" (provisional name)

Test vectors

No compression, no EC multiply

Test 1:

  • Passphrase: TestingOneTwoThree
  • Encrypted: 6PRVWUbkzzsbcVac2qwfssoUJAN1Xhrg6bNk8J7Nzm5H7kxEbn2Nh2ZoGg
  • Unencrypted (WIF): 5KN7MzqK5wt2TP1fQCYyHBtDrXdJuXbUzm4A9rKAteGu3Qi5CVR
  • Unencrypted (hex): CBF4B9F70470856BB4F40F80B87EDB90865997FFEE6DF315AB166D713AF433A5

Test 2:

  • Passphrase: Satoshi
  • Encrypted: 6PRNFFkZc2NZ6dJqFfhRoFNMR9Lnyj7dYGrzdgXXVMXcxoKTePPX1dWByq
  • Unencrypted (WIF): 5HtasZ6ofTHP6HCwTqTkLDuLQisYPah7aUnSKfC7h4hMUVw2gi5
  • Unencrypted (hex): 09C2686880095B1A4C249EE3AC4EEA8A014F11E6F986D0B5025AC1F39AFBD9AE

Compression, no EC multiply

Test 1:

  • Passphrase: TestingOneTwoThree
  • Encrypted: 6PYNKZ1EAgYgmQfmNVamxyXVWHzK5s6DGhwP4J5o44cvXdoY7sRzhtpUeo
  • Unencrypted (WIF): L44B5gGEpqEDRS9vVPz7QT35jcBG2r3CZwSwQ4fCewXAhAhqGVpP
  • Unencrypted (hex): CBF4B9F70470856BB4F40F80B87EDB90865997FFEE6DF315AB166D713AF433A5

Test 2:

  • Passphrase: Satoshi
  • Encrypted: 6PYLtMnXvfG3oJde97zRyLYFZCYizPU5T3LwgdYJz1fRhh16bU7u6PPmY7
  • Unencrypted (WIF): KwYgW8gcxj1JWJXhPSu4Fqwzfhp5Yfi42mdYmMa4XqK7NJxXUSK7
  • Unencrypted (hex): 09C2686880095B1A4C249EE3AC4EEA8A014F11E6F986D0B5025AC1F39AFBD9AE

EC multiply, no compression

Test 1:

  • Passphrase: TestingOneTwoThree
  • Passphrase code: passphrasepxFy57B9v8HtUsszJYKReoNDV6VHjUSGt8EVJmux9n1J3Ltf1gRxyDGXqnf9qm
  • Encrypted key: 6PfQu77ygVyJLZjfvMLyhLMQbYnu5uguoJJ4kMCLqWwPEdfpwANVS76gTX
  • Bitcoin address: 1PE6TQi6HTVNz5DLwB1LcpMBALubfuN2z2
  • Unencrypted private key (WIF): 5K4caxezwjGCGfnoPTZ8tMcJBLB7Jvyjv4xxeacadhq8nLisLR2
  • Unencrypted private key (hex): A43A940577F4E97F5C4D39EB14FF083A98187C64EA7C99EF7CE460833959A519

Test 2:

  • Passphrase: Satoshi
  • Passphrase code: passphraseoRDGAXTWzbp72eVbtUDdn1rwpgPUGjNZEc6CGBo8i5EC1FPW8wcnLdq4ThKzAS
  • Encrypted key: 6PfLGnQs6VZnrNpmVKfjotbnQuaJK4KZoPFrAjx1JMJUa1Ft8gnf5WxfKd
  • Bitcoin address: 1CqzrtZC6mXSAhoxtFwVjz8LtwLJjDYU3V
  • Unencrypted private key (WIF): 5KJ51SgxWaAYR13zd9ReMhJpwrcX47xTJh2D3fGPG9CM8vkv5sH
  • Unencrypted private key (hex): C2C8036DF268F498099350718C4A3EF3984D2BE84618C2650F5171DCC5EB660A

See Also

Retrieved from "https://en.bitcoin.it/w/index.php?title=BIP_0038&oldid=34542"